The structure of locally soluble groups in which all subgroups are pronormal is known, and many authors have investigated groups which are rich in pronormal subgroups. Here we prove that if a radical group Ghas pronormal deviation, which means that the set of its non-pronormal subgroups satisfies a very weak chain condition, then either Gis minimax or all its subgroups are pronormal. It follows that if a radical group has pronormal deviation, then its pronormal deviation is at most 1.
Groups with pronormal deviation
Alessio Russo
2023
Abstract
The structure of locally soluble groups in which all subgroups are pronormal is known, and many authors have investigated groups which are rich in pronormal subgroups. Here we prove that if a radical group Ghas pronormal deviation, which means that the set of its non-pronormal subgroups satisfies a very weak chain condition, then either Gis minimax or all its subgroups are pronormal. It follows that if a radical group has pronormal deviation, then its pronormal deviation is at most 1.File in questo prodotto:
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